Derivative and functional graph

Hello, everyone, I encountered a tough problem, urging help. Many thanks.

A curve, unknown its functional expression, with approximate 20 extreme points (including min and max), now know the first 10 extreme points (a1…a10) and f(a1-a10), monotony (first 10 points) is clear as well ,is it possible to work out either the rest extreme points or f(a),or both? Thanks.

Re: Derivative and functional graph

I don't know what you mean. You say there are 20 "extreme points" but also say of the first ten that "monotony is clear as well". What do you mean by "monotony"? That the function is monotone? That's impossible. If the function is monotone, then only its end points can be extreme points.

In any case, just knowing some points on a graph, even if they are "extreme points", tells you nothing about other points, unless you have some precise information about the function.